The present invention relates to a new and distinct variety of peach tree, Prunus persica var. nucipersica, which has been given the variety denomination ‘Crispdelice Sun’. This new tree produces fruit with a long shelf life without alteration both on the tree after growth completion and after harvesting, very good eating quality, clingstone flesh fruit for fresh market in August in the Pyrénées-Orientales departement, France. Contrast is made to ‘Mercil’ (O'Henry) U.S. Plant Pat. No. 2,964 to Grant Merrill (as indicated in U.S. Plant Pat. No. 4,508), ‘Merdame’ (Elegant Lady®) (U.S. Plant Pat. No. 4,399) peaches, standard varieties, for reliable description. ‘Crispdelice Sun’ is a promising candidate for commercial success in that it has fruit with very long shelf life without alteration after harvesting, and so a very durable fruit.